A wrappable textile sleeve for protecting a conductive elongate member against at least one of EMI, RFI or ESD and method of construction thereof is provided. The sleeve includes a plurality of warp filaments and at least one weft filament woven with one another to form a woven substrate. The woven substrate has opposite sides extending lengthwise between opposite ends. The opposite sides are wrappable about a central longitudinal axis into overlapping relation with one another to circumferentially enclose the elongate member within a cavity of the sleeve. At least some of the warp filaments are provided as generally flat, thin conductive filaments shield the conductive elongate member against the effects of EMI, RFI and/or ESD.